The basic information requirements for all routing models are:
A description of the channel. All routing models that are included in the program require a description of the channel. In some of the models, this description is implicit in parameters of the model. In others, the description is provided in more common terms: channel width, bed slope, cross-section shape, or the equivalent. The 8-point cross-section configuration is one of the cross section shapes available to describe the channel. The 8 pairs of x, y (distance, elevation) values are described spatially in the figure below. Coordinates 3 and 6 represent the left and right banks of the channel, respectively. Coordinates 4 and 5 are located within the channel. Coordinates 1 and 2 represent the left overbank and coordinates 7 and 8 represent the right overbank.
Energy-loss model parameters. All routing models incorporate some type of energy-loss model. The physically-based routing models, such as the kinematic-wave model and the Muskingum-Cunge model use Manning's equation and Manning's roughness coefficients (n values). Other models represent the energy loss empirically.
Initial conditions. All routing models require initial conditions: the flow (or stage) at the downstream cross section of a channel prior to the first time period. For example, the initial downstream flow could be estimated as the initial inflow, the baseflow within the channel at the start of the simulation, or the downstream flow likely to occur during a hypothetical event.
Boundary conditions. The boundary conditions for routing models are the upstream inflow, lateral inflow, and tributary inflow hydrographs. These may be observed historical events, or they may be computed with the precipitation-runoff models included in the program.
Available Channel Routing Methods
A total of eight different channel routing methods are available for use within HEC-HMS. These methods include:
Kinematic Wave78
79 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/lag-model 80 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/lag-and-k-model 81 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/modified-puls-model 82 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/muskingum-model 83 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/muskingum-cunge-model 84 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/normal-depth-model 85 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/straddle-stagger-model 86 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/transform/kinematic-wave-transform-model
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• Lag79 Lag and K80 Modified Puls81 Muskingum82 Muskingum-Cunge83 Normal Depth84 Straddle Stagger85
The following sections detail their unique concepts and uses.
Kinematic Wave Channel Routing Model
Basic Concepts and Equations
The derivation of the kinematic wave routing method is detailed within the Kinematic Wave Transform Model86 section. In summary, this method approximates the full unsteady flow equations by neglecting inertial and pressure forces. Specifically, the pressure gradient, convective acceleration, and local
acceleration terms within the momentum equation are ignored. This results in the following simplification:
100)
As shown within the previous equation, the energy gradient is assumed to be equal to the bottom slope.
Required Parameters
The parameters that are required to utilize this method within HEC-HMS are the initial condition, the reach length [ft or m], the bottom slope [ft/ft or m/m], Manning’s n roughness coefficient, the number of
subreaches, an index method and value, and a cross-section shape and parameters/dimensions. An optional invert can also be specified.
Two options for specifying the initial condition are included: outflow equals inflow and specified discharge [ft3/sec or m3/sec]. The first option assumes that the initial outflow is the same as the initial inflow to the reach from the upstream elements which is equivalent to the assumption of a steady-state initial condition.
The second option is most appropriate when there is observed streamflow data at the end of the reach.
As such, this method is only appropriate for use in steep channels (i.e. 10 ft/mi or greater) and does not recreate backwater effects.
The reach length should be set as the total length of the reach element while the bed slope should be set as the average bed slope for the entire reach. If the slope varies significantly throughout the stream
represented by the reach, it may be necessary to use multiple reaches with different slopes. The Manning's n roughness coefficient should be set as the average value for the whole reach. This value can be estimated using “reference” streams with established roughness coefficients or through calibration.
The number of subreaches is used in concert with the index method to determine the minimum distance step to use during routing calculations. Two options for specifying an index method are included: flow [ft3/s or m3/s] and celerity [ft/s or m/s]. When index flow is selected, the user-entered flow rate is converted to an equivalent celerity using the cross-section shape of the reach. When the index celerity method is selected, the travel time is computed directly from the specified value. The distance step is first estimated from the travel time. If the distance step is greater than the reach length divided by the number of subreaches, then the distance step is decreased.
Five options are provided for specifying the cross-section shape: circle, deep, rectangle, trapezoid, and triangle. The circle shape is not meant to be used for pressure flow or pipe networks, but is suitable for representing a free surface inside a pipe. The deep shape should only be used for flow conditions where the flow depth is approximately equal to the flow width. Depending on the shape you choose, additional
information will have to be entered to describe the size of the cross-section shape. This information may include a diameter (circle) [ft or m], bottom width (deep, rectangle, and/or trapezoid) [ft or m], or side slope (trapezoid and triangle) [ft/ft or m/m]. In all cases, cross-section shapes must be defined in such a way that all possible flow depths that will be simulated will be completely confined within the defined shape.
Many of the aforementioned parameters are typically estimated using GIS. However, field survey data may be necessary to accurately determine reach lengths, bed slopes, and/or cross-section shape parameters.
Lag Model
Basic Concepts and Equations
This is the simplest of the routing models in HEC-HMS. Using the Lag model, the outflow hydrograph is simply the inflow hydrograph, but with all ordinates translated (lagged in time) by a specified duration. The flows are not attenuated, so the shape is not changed.
Mathematically, the downstream ordinates are computed by:
101)
where = outflow hydrograph ordinate at time t; = inflow hydrograph ordinate at time t; and lag = time by which the inflow ordinates are to be lagged.
This method does not include any representation of attenuation or diffusion processes.
Consequently, it is best suited to short stream segments with a predicable travel time that doesn't vary with changing conditions.
The lag model is a special case of other models, as its results can be duplicated if parameters of those other models are carefully chosen. For example, if X = 0.50 and K = in the Muskingum model, the computed outflow hydrograph will equal the inflow hydrograph lagged by K.
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88 https://www.hec.usace.army.mil/confluence/hmsdocs/hmstrm/channel-flow/muskingum-model
Required Parameters
The parameters that are required to utilize this method within HEC-HMS are the initial condition and a lag time [minutes]. Two options for specifying the initial condition are included: outflow equals inflow and specified discharge [ft3/sec or m3/sec]. The first option assumes that the initial outflow is the same as the initial inflow to the reach from the upstream elements which is equivalent to the assumption of a steady- state initial condition. The second option is most appropriate when there is observed streamflow data at the end of the reach. Lag time is the amount of time that the inflow hydrograph will be translated.
Lag and K Model
Basic Concepts and Equations
The Lag and K routing method is a hydrologic storage routing method based on a graphical routing
technique that is extensively used by the National Weather Service (NWS) (Linsley, Kohler, & Paulhus, 1982).
Within this method, lag and K represent translation and attenuation, respectively. The method is a special case of the Muskingum88 method where channel storage is represented by the prism component alone with no wedge storage (i.e. Muskingum X = 0). The following equation is combined with inflow vs. translation and outflow vs. attenuation functions in order to solve for outflow:
102)
where dS/dt = time rate of change of water in storage at time t; It = average inflow to storage at time t; and Ot
= outflow from storage at time t.
Required Parameters
The parameters that are required to utilize this method within HEC-HMS are the initial condition, a lag method and value or function, and a K method and value or function. Two options for specifying the initial condition are included: outflow equals inflow and specified discharge [ft3/sec or m3/sec]. The first option assumes that the initial outflow is the same as the initial inflow to the reach from the upstream elements which is equivalent to the assumption of a steady-state initial condition. The second option is most appropriate when there is observed streamflow data at the end of the reach. Two options for specifying a
A tutorial describing an example application of this channel routing method, including parameter estimation and calibration, can be found here: Applying the Lag Routing Method87.
The lack of wedge storage means that the method should only be used for slowly varying flood waves. Also, this method does not account for complex flow conditions such as backwater effects and/or hydraulic structures.
lag method are included: Constant Lag [hours] and Variable Lag. When using the Variable Lag option, an Inflow-Lag function (which is a paired data object) must be specified. Similarly, two options for specifying a K method are included: Constant K [hours] and Variable K. When using the Variable K option, an Outflow- Attenuation function (which is a paired data object) must be specified. These relationships are typically derived through evaluation of historical flood hydrographs. Care must be exercised when using lag functions with multiple intercepts (i.e., lag is the same for more than one flow rate) as this may result in numerically attenuated peak flow rates.
Modified Puls Model
Basic Concepts and Equations
The Modified Puls routing method, also known as storage routing or level-pool routing, is based upon a finite difference approximation of the continuity equation, coupled with an empirical representation of the
momentum equation (Chow, 1964; Henderson, 1966). For the Modified Puls model, the continuity equation is written as
103)
This simplification assumes that the lateral inflow is insignificant, and it allows width to change with respect to location. Rearranging this equation and incorporating a finite-difference approximation for the partial derivatives yields:
104)
where = average upstream flow (inflow to reach) during a period ; = average downstream flow (outflow from reach) during the same period; and = change in storage in the reach during the period.
Using a simple backward differencing scheme and rearranging the result to isolate the unknown values yields:
105)
in which and = inflow hydrograph ordinates at times t-1 and t, respectively; and = outflow hydrograph ordinates at times t-1 and t, respectively; and and = storage in reach at times t-1 and t, respectively. At time t, all terms on the right-hand side of this equation are known, and terms on the left-hand side are to be found. Thus, the equation has two unknowns at time t: and . A functional relationship between storage and outflow is required to solve Equation 3. Once that function is established, it is
substituted into Equation 3, reducing the equation to a nonlinear equation with a single unknown, . This equation is solved recursively by the program, using a trial-and-error procedure. Note that at the first time t, the outflow at time t-1 must be specified to permit recursive solution of the equation; this outflow is the initial outflow condition for the storage routing model.
If the storage vs. discharge relationships are carefully constructed using a hydraulic model that includes bridges and/or other hydraulic structures, this method can simulate backwater effects and the impacts of hydraulic structures so long as the effects/impacts are fully contained within the reach.